Limit theorems on sizes of trees in a random unlabelled forest

We describe the asymptotic behaviour of the maximum size of a tree and of the number of trees of a given size in a random forest of $N$ trees and $n$ unlabelled vertices in all domains where $N$, $n$ tend to infinity.
This research was supported by the program of the President of Russian Federation of supporting leading scientific schools, grant 1758.2003.1.